If I had the opportunity, I would set up a system whereby the Eastern Germans would be hired to tutor the immigrants in all of Germany in German language skills either by telephone or by computer in return for higher living assistance.  

As native-speaking Germans they would have a natural advantage but might require some training.

German society as a whole would improve its productivity and better integrate the "left behind" groups into society.

It's a plan that I would spend more time developing maybe to propose as some sort of subsidised business plan but I would require some help.